circle.js

import {cartesian, cartesianAddInPlace, cartesianCross, cartesianDot, cartesianScale, spherical} from "../cartesian";
import {circleStream} from "../circle";
import {abs, cos, epsilon, pi, radians, sqrt} from "../math";
import pointEqual from "../pointEqual";
import clip from "./index";

export default function(radius) {
  var cr = cos(radius),
      delta = 6 * radians,
      smallRadius = cr > 0,
      notHemisphere = abs(cr) > epsilon; // TODO optimise for this common case

  function interpolate(from, to, direction, stream) {
    circleStream(stream, radius, delta, direction, from, to);
  }

  function visible(lambda, phi) {
    return cos(lambda) * cos(phi) > cr;
  }

  // Takes a line and cuts into visible segments. Return values used for polygon
  // clipping: 0 - there were intersections or the line was empty; 1 - no
  // intersections 2 - there were intersections, and the first and last segments
  // should be rejoined.
  function clipLine(stream) {
    var point0, // previous point
        c0, // code for previous point
        v0, // visibility of previous point
        v00, // visibility of first point
        clean; // no intersections
    return {
      lineStart: function() {
        v00 = v0 = false;
        clean = 1;
      },
      point: function(lambda, phi) {
        var point1 = [lambda, phi],
            point2,
            v = visible(lambda, phi),
            c = smallRadius
              ? v ? 0 : code(lambda, phi)
              : v ? code(lambda + (lambda < 0 ? pi : -pi), phi) : 0;
        if (!point0 && (v00 = v0 = v)) stream.lineStart();
        // Handle degeneracies.
        // TODO ignore if not clipping polygons.
        if (v !== v0) {
          point2 = intersect(point0, point1);
          if (!point2 || pointEqual(point0, point2) || pointEqual(point1, point2)) {
            point1[0] += epsilon;
            point1[1] += epsilon;
            v = visible(point1[0], point1[1]);
          }
        }
        if (v !== v0) {
          clean = 0;
          if (v) {
            // outside going in
            stream.lineStart();
            point2 = intersect(point1, point0);
            stream.point(point2[0], point2[1]);
          } else {
            // inside going out
            point2 = intersect(point0, point1);
            stream.point(point2[0], point2[1]);
            stream.lineEnd();
          }
          point0 = point2;
        } else if (notHemisphere && point0 && smallRadius ^ v) {
          var t;
          // If the codes for two points are different, or are both zero,
          // and there this segment intersects with the small circle.
          if (!(c & c0) && (t = intersect(point1, point0, true))) {
            clean = 0;
            if (smallRadius) {
              stream.lineStart();
              stream.point(t[0][0], t[0][1]);
              stream.point(t[1][0], t[1][1]);
              stream.lineEnd();
            } else {
              stream.point(t[1][0], t[1][1]);
              stream.lineEnd();
              stream.lineStart();
              stream.point(t[0][0], t[0][1]);
            }
          }
        }
        if (v && (!point0 || !pointEqual(point0, point1))) {
          stream.point(point1[0], point1[1]);
        }
        point0 = point1, v0 = v, c0 = c;
      },
      lineEnd: function() {
        if (v0) stream.lineEnd();
        point0 = null;
      },
      // Rejoin first and last segments if there were intersections and the first
      // and last points were visible.
      clean: function() {
        return clean | ((v00 && v0) << 1);
      }
    };
  }

  // Intersects the great circle between a and b with the clip circle.
  function intersect(a, b, two) {
    var pa = cartesian(a),
        pb = cartesian(b);

    // We have two planes, n1.p = d1 and n2.p = d2.
    // Find intersection line p(t) = c1 n1 + c2 n2 + t (n1 ⨯ n2).
    var n1 = [1, 0, 0], // normal
        n2 = cartesianCross(pa, pb),
        n2n2 = cartesianDot(n2, n2),
        n1n2 = n2[0], // cartesianDot(n1, n2),
        determinant = n2n2 - n1n2 * n1n2;

    // Two polar points.
    if (!determinant) return !two && a;

    var c1 =  cr * n2n2 / determinant,
        c2 = -cr * n1n2 / determinant,
        n1xn2 = cartesianCross(n1, n2),
        A = cartesianScale(n1, c1),
        B = cartesianScale(n2, c2);
    cartesianAddInPlace(A, B);

    // Solve |p(t)|^2 = 1.
    var u = n1xn2,
        w = cartesianDot(A, u),
        uu = cartesianDot(u, u),
        t2 = w * w - uu * (cartesianDot(A, A) - 1);

    if (t2 < 0) return;

    var t = sqrt(t2),
        q = cartesianScale(u, (-w - t) / uu);
    cartesianAddInPlace(q, A);
    q = spherical(q);

    if (!two) return q;

    // Two intersection points.
    var lambda0 = a[0],
        lambda1 = b[0],
        phi0 = a[1],
        phi1 = b[1],
        z;

    if (lambda1 < lambda0) z = lambda0, lambda0 = lambda1, lambda1 = z;

    var delta = lambda1 - lambda0,
        polar = abs(delta - pi) < epsilon,
        meridian = polar || delta < epsilon;

    if (!polar && phi1 < phi0) z = phi0, phi0 = phi1, phi1 = z;

    // Check that the first point is between a and b.
    if (meridian
        ? polar
          ? phi0 + phi1 > 0 ^ q[1] < (abs(q[0] - lambda0) < epsilon ? phi0 : phi1)
          : phi0 <= q[1] && q[1] <= phi1
        : delta > pi ^ (lambda0 <= q[0] && q[0] <= lambda1)) {
      var q1 = cartesianScale(u, (-w + t) / uu);
      cartesianAddInPlace(q1, A);
      return [q, spherical(q1)];
    }
  }

  // Generates a 4-bit vector representing the location of a point relative to
  // the small circle's bounding box.
  function code(lambda, phi) {
    var r = smallRadius ? radius : pi - radius,
        code = 0;
    if (lambda < -r) code |= 1; // left
    else if (lambda > r) code |= 2; // right
    if (phi < -r) code |= 4; // below
    else if (phi > r) code |= 8; // above
    return code;
  }

  return clip(visible, clipLine, interpolate, smallRadius ? [0, -radius] : [-pi, radius - pi]);
}